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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Tue, 21 Dec 2010 16:38:49 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292949412hox639wkmqqmhfa.htm/, Retrieved Sun, 19 May 2024 17:43:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113737, Retrieved Sun, 19 May 2024 17:43:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [WS8 Autocorolation] [2010-12-01 09:55:45] [b84bdc9bd81e1f02ca0dcc4710c1b790]
-   PD    [(Partial) Autocorrelation Function] [ACF] [2010-12-21 15:58:54] [fc9068db680cd880760a7c0fccd81a61]
- R         [(Partial) Autocorrelation Function] [VRM] [2010-12-21 16:31:09] [fc9068db680cd880760a7c0fccd81a61]
- RM            [Variance Reduction Matrix] [VRM] [2010-12-21 16:38:49] [a8abc7260f3c847aeac0a796e7895a2e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113737&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113737&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113737&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	2005930735.29139	Range	150906	Trim Var.	1625687765.12740
V(Y[t],d=1,D=0)	2633598.51915709	Range	9896	Trim Var.	1478204.43040293
V(Y[t],d=2,D=0)	4730646.05397301	Range	11846	Trim Var.	2293698.28631258
V(Y[t],d=3,D=0)	13980338.0407323	Range	20441	Trim Var.	7490707.21073672
V(Y[t],d=0,D=1)	20801085.1080863	Range	22435	Trim Var.	11341065.8215511
V(Y[t],d=1,D=1)	1595848.17161172	Range	6407	Trim Var.	792223.369097709
V(Y[t],d=2,D=1)	2293963.63918969	Range	9526	Trim Var.	1010805.21882465
V(Y[t],d=3,D=1)	6577449.5817628	Range	18060	Trim Var.	2958899.65250305
V(Y[t],d=0,D=2)	43745445.9226722	Range	31974	Trim Var.	22397876.5054504
V(Y[t],d=1,D=2)	4184423.53179056	Range	12324	Trim Var.	2233714.9788422
V(Y[t],d=2,D=2)	7000301.85702341	Range	18060	Trim Var.	2766013.63098464
V(Y[t],d=3,D=2)	19710557.9858364	Range	28737	Trim Var.	9022796.24197531

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2005930735.29139 & Range & 150906 & Trim Var. & 1625687765.12740 \tabularnewline
V(Y[t],d=1,D=0) & 2633598.51915709 & Range & 9896 & Trim Var. & 1478204.43040293 \tabularnewline
V(Y[t],d=2,D=0) & 4730646.05397301 & Range & 11846 & Trim Var. & 2293698.28631258 \tabularnewline
V(Y[t],d=3,D=0) & 13980338.0407323 & Range & 20441 & Trim Var. & 7490707.21073672 \tabularnewline
V(Y[t],d=0,D=1) & 20801085.1080863 & Range & 22435 & Trim Var. & 11341065.8215511 \tabularnewline
V(Y[t],d=1,D=1) & 1595848.17161172 & Range & 6407 & Trim Var. & 792223.369097709 \tabularnewline
V(Y[t],d=2,D=1) & 2293963.63918969 & Range & 9526 & Trim Var. & 1010805.21882465 \tabularnewline
V(Y[t],d=3,D=1) & 6577449.5817628 & Range & 18060 & Trim Var. & 2958899.65250305 \tabularnewline
V(Y[t],d=0,D=2) & 43745445.9226722 & Range & 31974 & Trim Var. & 22397876.5054504 \tabularnewline
V(Y[t],d=1,D=2) & 4184423.53179056 & Range & 12324 & Trim Var. & 2233714.9788422 \tabularnewline
V(Y[t],d=2,D=2) & 7000301.85702341 & Range & 18060 & Trim Var. & 2766013.63098464 \tabularnewline
V(Y[t],d=3,D=2) & 19710557.9858364 & Range & 28737 & Trim Var. & 9022796.24197531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113737&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2005930735.29139[/C][C]Range[/C][C]150906[/C][C]Trim Var.[/C][C]1625687765.12740[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2633598.51915709[/C][C]Range[/C][C]9896[/C][C]Trim Var.[/C][C]1478204.43040293[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]4730646.05397301[/C][C]Range[/C][C]11846[/C][C]Trim Var.[/C][C]2293698.28631258[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]13980338.0407323[/C][C]Range[/C][C]20441[/C][C]Trim Var.[/C][C]7490707.21073672[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]20801085.1080863[/C][C]Range[/C][C]22435[/C][C]Trim Var.[/C][C]11341065.8215511[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1595848.17161172[/C][C]Range[/C][C]6407[/C][C]Trim Var.[/C][C]792223.369097709[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2293963.63918969[/C][C]Range[/C][C]9526[/C][C]Trim Var.[/C][C]1010805.21882465[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6577449.5817628[/C][C]Range[/C][C]18060[/C][C]Trim Var.[/C][C]2958899.65250305[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]43745445.9226722[/C][C]Range[/C][C]31974[/C][C]Trim Var.[/C][C]22397876.5054504[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4184423.53179056[/C][C]Range[/C][C]12324[/C][C]Trim Var.[/C][C]2233714.9788422[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]7000301.85702341[/C][C]Range[/C][C]18060[/C][C]Trim Var.[/C][C]2766013.63098464[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]19710557.9858364[/C][C]Range[/C][C]28737[/C][C]Trim Var.[/C][C]9022796.24197531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113737&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113737&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	2005930735.29139	Range	150906	Trim Var.	1625687765.12740
V(Y[t],d=1,D=0)	2633598.51915709	Range	9896	Trim Var.	1478204.43040293
V(Y[t],d=2,D=0)	4730646.05397301	Range	11846	Trim Var.	2293698.28631258
V(Y[t],d=3,D=0)	13980338.0407323	Range	20441	Trim Var.	7490707.21073672
V(Y[t],d=0,D=1)	20801085.1080863	Range	22435	Trim Var.	11341065.8215511
V(Y[t],d=1,D=1)	1595848.17161172	Range	6407	Trim Var.	792223.369097709
V(Y[t],d=2,D=1)	2293963.63918969	Range	9526	Trim Var.	1010805.21882465
V(Y[t],d=3,D=1)	6577449.5817628	Range	18060	Trim Var.	2958899.65250305
V(Y[t],d=0,D=2)	43745445.9226722	Range	31974	Trim Var.	22397876.5054504
V(Y[t],d=1,D=2)	4184423.53179056	Range	12324	Trim Var.	2233714.9788422
V(Y[t],d=2,D=2)	7000301.85702341	Range	18060	Trim Var.	2766013.63098464
V(Y[t],d=3,D=2)	19710557.9858364	Range	28737	Trim Var.	9022796.24197531

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()

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Input Parameters & R Code